{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Rabi Flopping\n", "\n", "This example covers Rabi flopping of a single spin in a magnetic field. We'll make a spin with quantum number $F=1/2$, place it in a magnetic field to split the states, then evolve it to watch the spin rotate." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import pylcp\n", "from pylcp.common import spherical2cart, cart2spherical" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Define the problem\n", "In this example, we include only one manifold (the ground manifold) simply because we do not need to worry about lasers and damping. \n", "We also want to create the spin operator $\\mathbf{F}=-\\boldsymbol{\\mu}/(\\mu_B g_F)$, which tells us which direction the spin is pointing on average. Combined with `obe.observable()`, we calculate $\\langle \\mathbf{F} \\rangle$. Note that in `pylcp`, $g_F > 0$ implies a magnetic moment $\\boldsymbol{\\mu}$ that is antialigned with $\\mathbf{F}$. This convention is standard when the magnetic moment is dominated by the electron. In this configuration, the spin will rotate counter-clockwise when viewed from the tip of the magnetic field vector." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "gF = 1 \n", "H_0, mu_q = pylcp.hamiltonians.singleF(1/2, gF=gF, muB=1)\n", "\n", "# Construct operators for calculation of expectation values of spin (F) and mu:\n", "mu = spherical2cart(mu_q)\n", "F = -mu/gF # Note that muB=1 \n", "\n", "hamiltonian = pylcp.hamiltonian()\n", "hamiltonian.add_H_0_block('g', H_0)\n", "hamiltonian.add_mu_q_block('g', mu_q)\n", "\n", "magField = pylcp.constantMagneticField(np.array([1., 0., 0.]))\n", "laserBeams = {}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Evolve with $B=(1, 0, 0)$\n", "\n", "This should make it rotate in the $\\hat{y}$-$\\hat{z}$ plane. After $t = \\pi \\hbar \\mu_B B$, it should end up along $-\\hat{y}$, if $g_F>0$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "obe = pylcp.obe(laserBeams, magField, hamiltonian, transform_into_re_im=False)\n", "pop = np.zeros((H_0.shape[0],))\n", "pop[-1] = 1\n", "\n", "obe.set_initial_rho_from_populations(pop)\n", "obe.evolve_density([0, np.pi/2], t_eval=np.linspace(0, np.pi/2, 51))\n", "avF = obe.observable(F)\n", "\n", "fig, ax = plt.subplots(1, 1)\n", "\n", "lbls = ['$\\\\langle F_x\\\\rangle$', '$\\\\langle F_y\\\\rangle$', '$\\\\langle F_z\\\\rangle$']\n", "[ax.plot(obe.sol.t, avF[ii], label=lbls[ii]) for ii in range(3)]\n", "ax.set_xlabel('$t/(\\hbar \\mu_B B)$')\n", "ax.set_ylabel('$\\langle \\\\mathbf{F}\\\\rangle$')\n", "ax.legend(fontsize=8);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Evolve again with $B=(0, 0, 1)$\n", "\n", "This should make it rotate in the $\\hat{x}$-$\\hat{y}$ plane, couter clockwise when viewed from $+\\hat{z}$.\n", "\n", "Note that rather than redefining the OBEs, I just replaced its internal `magField` variable. This is possible, because the OBEs construction in `pylcp` are only dependent on the Hamiltonian, not the external fields." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "obe.set_initial_rho(obe.sol.rho[:, :, -1])\n", "obe.magField = pylcp.magField(lambda R: np.array([0., 0., 1.]))\n", "obe.evolve_density([0, 2*np.pi], t_eval=np.linspace(0, 2*np.pi, 51))\n", "avF = obe.observable(F)\n", "\n", "fig, ax = plt.subplots(1, 1)\n", "[ax.plot(obe.sol.t, avF[ii], label=lbls[ii]) for ii in range(3)]\n", "ax.set_xlabel('$t/(\\hbar \\mu_B B)$')\n", "ax.set_ylabel('$\\langle \\\\mathbf{F}\\\\rangle$')\n", "ax.legend(fontsize=8);" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 4 }